Skewed normal cloud modified whale optimization algorithm for degree reduction of S-λ curves

Abstract

Whale optimization algorithm (WOA) is a new meta-heuristic algorithm for mathematical description of the foraging behavior of whales. Cloud model (CM) is an effective model to describe cognitive uncertainty, at the same time, it can comprehensively describe the randomness and fuzziness in uncertain phenomena. Skew normal distribution (SND) can better describe the biological behavior situation when the environment changes. In this paper, a new skew normal cloud model (SNCM) is established in the first place by combining the CM with the SND and the skew normal membership function to describe the fuzziness and randomness of environmental change. Secondly,because of the randomness and fuzziness of the whales’ foraging behavior, in order to improve the exploration and exploitation ability of WOA,an emendatory WOA based on the skew normal cloud (SNC) is proposed through the use of the SNCM to modify the shrinking encircling and spiral update strategies of WOA, and the adaptive position and skewness parameters in the SNC are designed to increase the exploration capability in prophase and the exploitation capability in anaphase. Lastly,the experimental results of the complex CEC2017 test set verify the effectiveness of the emendatory WOA under different strategies and different dimensions and different improved WOA algorithm and other representative heuristic algorithms. Three degree reduction of S\u2009−\u2009λ curves verify the practicability of the the modified WOA in the field of curve design.